Date of Award
2006
Degree Type
Thesis
Degree Name
Doctor of Philosophy
Program
Statistics and Actuarial Sciences
Supervisor
Dr. A. Ian MacLeod
Second Advisor
Dr. Guangyong Zou
Abstract
Portmanteau tests are standard diagnostic tools under the Box-Jenkins framework and are widely used in practice. This thesis developed new portmanteau tests for diagnostic checking several time series models, such as multivariate time series with autoregressive conditional heterscedastic errors and autoregressive models with stable Paretian errors. Using a proposed Monte-Carlo test procedure, I found that the size distortion of the proposed tests is negligible and that the proposed tests are usually more powerful than usual portmanteau tests. A nonparametric bootstrap test procedure is also used to check randomness of a time series. It is found that the size distortion of portmanteau tests with the boot strap test procedure is negligible except for highly skewed distributions and extremely heavy tailed distributions. In such asymmetric distributions, the use of a Box-Cox transformation on the data prior to bootstrapping eliminates the size distortion prob lem. In all, in this thesis, new portmanteau tests based on the generalized variance of standardized residuals were developed and found to be more powerful empirically than usual portmanteau tests. It is also found that the use of the Monte-Carlo test or bootstrap test procedure eliminates the size distortion problem which is the common criticism on the use of portmanteau tests.
Recommended Citation
Lin, Jen-Wen, "ESSAYS ON DIAGNOSTIC CHECKS IN TIME SERIES" (2006). Digitized Theses. 5104.
https://ir.lib.uwo.ca/digitizedtheses/5104